Quantum Hall liquid, Josephson effect, and hierarchy in a double-layer electron system

Ezawa, Zyun F.; Iwazaki, Aiichi

doi:10.1103/physrevb.47.7295

Cited by 137 publications

(91 citation statements)

References 31 publications

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“…The description of the system with each particle having a definite spin polarization can be given by an effective Chern-Simons theory [15] also, in the so-called U(1)×U(1) formulation with two abelian gauge fields a µ ↑ and a µ ↓ [16]. The Chern-Simons constraints that it contains are 4) which are simple generalizations of the constraint in the Laughlin case ( ∇ × a = 2πmρ).…”

Section: Halperin State and Gluing Of Charge And Spinmentioning

confidence: 99%

Invariant structure of the hierarchy theory of fractional quantum Hall states with spin

Milovanović

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1997

Phys. Rev. B

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We describe the invariant structure common to abelian fractional quantum Hall effect systems with spin. It appears in a generalization of the lattice description of the polarized hierarchy that encompasses both partially polarized and unpolarized ground state systems. We formulate, using the spin-charge decomposition, conditions that should be satisfied so that the description is SU(2) invariant. In the case of the spin-singlet hierarchy construction, we find that there are as many SU(2) symmetries as there are levels in the construction. Various formalisms used before for hierarchies (field-theoretic, algebraic, and wave-functions) are also used to show the existence of a spin and charge lattice for the systems with spin. The "gluing" of the charge and spin degrees of freedom in their bulk is described by the gluing theory of lattices. The lowenergy field theories and corresponding quantum Hall lattices should serve as a starting point for the discussion of the stability of these systems.

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Section: Halperin State and Gluing Of Charge And Spinmentioning

confidence: 99%

Invariant structure of the hierarchy theory of fractional quantum Hall states with spin

Milovanović

Read

1997

Phys. Rev. B

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“…This collective phase may be viewed in several equivalent ways, including as a Bose condensate of interlayer excitons [9] or a pseudospin ferromagnet [10]. In addition to the fascinating phenomena already observed in this collective phase, there remains the prediction that the system should possess counterflow superfluidity: equal but oppositely directed currents in the two layers should produce no dissipation (in linear response) at low temperatures [11,12,13,14]. Dissipationless transport is, of course, a hallmark of the ordinary QHE.…”

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confidence: 99%

Vanishing Hall Resistance at High Magnetic Field in a Double-Layer Two-Dimensional Electron System

Kellogg

Eisenstein

Pfeiffer³

et al. 2004

Phys. Rev. Lett.

301

326

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At total Landau level filling factor νtot = 1 a double layer two-dimensional electron system with small interlayer separation supports a collective state possessing spontaneous interlayer phase coherence. This state exhibits the quantized Hall effect when equal electrical currents flow in parallel through the two layers. In contrast, if the currents in the two layers are equal, but oppositely directed, both the longitudinal and Hall resistances of each layer vanish in the low temperature limit. This finding supports the prediction that the ground state at νtot = 1 is an excitonic superfluid.The Hall effect is possibly the most widely observed phenomenon in solid state physics [1]. Owing to the Lorentz force, an ordinary current-carrying conductor in a magnetic field develops a voltage drop V H transverse to both the current I and the field. This Hall voltage is directly proportional to the magnetic field and offers a useful measure of the concentration and sign of the constituent particles responsible for conduction in the material. In more exotic systems the Hall resistance R H = V H /I can deviate strongly from this simple dependence. For example, in two-dimensional electron systems (2DES) R H exhibits ranges of magnetic field over which it is constant and precisely equal to the quantum of resistance h/e 2 divided by either an integer [2] or certain rational fractions [3]. These quantized Hall effects (QHE) reflect the presence of an energy gap in the system, due either to Landau quantization of the cyclotron orbits of the electrons or to the strong interactions between electrons in a partially filled Landau band. In superconductors, where a coherent collective electronic state is present, the Hall resistance vanishes altogether [4].In this paper we report low temperature measurements of the Hall and longitudinal resistances of a double layer 2DES in a strong perpendicular magnetic field B. Our focus is on the situation in which the total electron density N tot of the double layer system is equal to the degeneracy eB/h of a single spin-resolved Landau level produced by the magnetic field. It is well known [5] that in this ν tot = hN tot /eB = 1 case the system possesses an unusual strongly correlated phase when the separation between the two layers is less than a critical value. Owing to interlayer Coulomb interactions the critical layer separation remains non-zero even in the limit of arbitrarily weak tunneling between the layers. In this zero tunneling limit the electron system exhibits a quantized Hall effect [6] with R H = h/e 2 , a dramatically enhanced and sharply resonant zero bias tunneling conductance [7], and exact quantization of the Hall component of Coulomb drag between the layers [8]. It is well-established theoretically that the many-electron state responsible for these phe- nomena possesses an unusual broken symmetry: spontaneous interlayer phase coherence. This collective phase may be viewed in several equivalent ways, including as a Bose condensate of interlayer excitons [9] or a pseudospin f...

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“…Both Coulomb interactions and interlayer tunneling contribute to the strength of this QHE but there is strong evidence from experiment [3,7] and theory [1,8] that the incompressibility survives in the limit of zero tunneling. This remarkable collective state exhibits a broken symmetry [9][10][11][12], spontaneous interlayer phase coherence, and may be viewed as a kind of easy-plane ferromagnet. The magnetization of this ferromagnet exists in a pseudospin space; electrons in one layer are pseudospin up, while those in the other layer are pseudospin down.…”

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confidence: 99%

Resonantly Enhanced Tunneling in a Double Layer Quantum Hall Ferromagnet

Spielman

Eisenstein

Pfeiffer³

et al. 2000

Phys. Rev. Lett.

469

646

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The tunneling conductance between two parallel 2D electron systems has been measured in a regime of strong interlayer Coulomb correlations. At total Landau level filling n T 1 the tunnel spectrum changes qualitatively when the boundary separating the compressible phase from the ferromagnetic quantized Hall state is crossed. A huge resonant enhancement replaces the strongly suppressed equilibrium tunneling characteristic of weakly coupled layers. The possible relationship of this enhancement to the Goldstone mode of the broken symmetry ground state is discussed. PACS numbers: 71.10.Pm, 73.40.Hm, 73.40.Gk When two parallel two-dimensional electron systems (2DES) are sufficiently close together, interlayer Coulomb interactions can produce collective states which have no counterpart in the individual 2D systems [1][2][3]. One of the simplest, yet most interesting, examples occurs when the total electron density, N T , equals the degeneracy, eB͞h, of a single spin-resolved Landau level produced by a magnetic field B. In the balanced case (i.e., with layer densities N 1 N 2 N T ͞2), the Landau level filling factor of each layer viewed separately is n hN T ͞2eB 1͞2. If the separation d between the layers is large, they behave independently and are well described as gapless composite fermion liquids. No quantized Hall effect (QHE) is seen. On the other hand, as d is reduced, the system undergoes a quantum phase transition [4-6] to an incompressible state best described by the total filling factor n T 1͞2 1 1͞2 1. A quantized Hall plateau now appears at r xy h͞e 2 . Both Coulomb interactions and interlayer tunneling contribute to the strength of this QHE but there is strong evidence from experiment [3,7] and theory [1,8] that the incompressibility survives in the limit of zero tunneling. This remarkable collective state exhibits a broken symmetry [9][10][11][12], spontaneous interlayer phase coherence, and may be viewed as a kind of easy-plane ferromagnet. The magnetization of this ferromagnet exists in a pseudospin space; electrons in one layer are pseudospin up, while those in the other layer are pseudospin down. Numerous interesting properties are anticipated, including linearly dispersing Goldstone collective modes (i.e., pseudospin waves), a finite temperature Kosterlitz-Thouless transition, dissipationless transport for currents directed oppositely in the two layers, and bizarre topological defects in the pseudospin field [9][10][11][12][13]. To date, most experimental results on this system have derived from electrical transport measurements [3,4,7,14,15] although recently an optical study has been reported [16].In this paper we report on a new study of the double layer n T 1 ferromagnetic quantum Hall state, and its transition at large layer separation to a compressible phase, using the method of tunneling spectroscopy. Earlier experiments have shown that there is a strong suppression of the equilibrium tunneling between two widely separated parallel 2DESs at high magnetic field [17,18]. This suppression is a ...

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Quantum Hall liquid, Josephson effect, and hierarchy in a double-layer electron system

Cited by 137 publications

References 31 publications

Invariant structure of the hierarchy theory of fractional quantum Hall states with spin

Invariant structure of the hierarchy theory of fractional quantum Hall states with spin

Vanishing Hall Resistance at High Magnetic Field in a Double-Layer Two-Dimensional Electron System

Resonantly Enhanced Tunneling in a Double Layer Quantum Hall Ferromagnet

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